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SageMath
E = EllipticCurve("fu1")
E.isogeny_class()
Elliptic curves in class 80850fu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 80850.gf4 | 80850fu1 | \([1, 0, 0, -1166838, -649551708]\) | \(-95575628340361/43812679680\) | \(-80539342994880000000\) | \([2]\) | \(3538944\) | \(2.5261\) | \(\Gamma_0(N)\)-optimal |
| 80850.gf3 | 80850fu2 | \([1, 0, 0, -20374838, -35396823708]\) | \(508859562767519881/62240270400\) | \(114414149567025000000\) | \([2, 2]\) | \(7077888\) | \(2.8726\) | |
| 80850.gf2 | 80850fu3 | \([1, 0, 0, -22089838, -29087338708]\) | \(648474704552553481/176469171805080\) | \(324397212401497764375000\) | \([2]\) | \(14155776\) | \(3.2192\) | |
| 80850.gf1 | 80850fu4 | \([1, 0, 0, -325987838, -2265454884708]\) | \(2084105208962185000201/31185000\) | \(57326313515625000\) | \([2]\) | \(14155776\) | \(3.2192\) |
Rank
sage: E.rank()
The elliptic curves in class 80850fu have rank \(0\).
Complex multiplication
The elliptic curves in class 80850fu do not have complex multiplication.Modular form 80850.2.a.fu
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
